リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「Hardy-Sobolev inequalities in the half space (Theory of function spaces and related topics)」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

Hardy-Sobolev inequalities in the half space (Theory of function spaces and related topics)

Mizuta, Yoshihiro Shimomura, Tetsu 京都大学

2023.05

概要

Our aim is to establish Hardy-Sobolev inequalities for Sobolev functions in Herz-Morrey spaces, which extend the classical Hardy inequalities in the L[p] Lebesgue space.

参考文献

[1] D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer,

1996.

[2] D. R. Adams and J. Xiao, Morrey spaces in harmonic analysis, Ark. Mat. 50 (2012),

no. 2, 201-230.

[3] V. I. Burenkov, A. Gogatishvili, V. S. Guliyev and R. Ch. Mustafayev, Boundedness

of the Riesz potential in local Morrey-type spaces, Potential Anal. 35 (2011), no. 1,

67-87.

[4] V. I. Burenkov and V. S. Guliyev, Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces, Potential Anal. 30 (2009),

no. 3, 211-249.

[5] H. G. Feichtinger and F. Weisz, Herz spaces and summability of Fourier transforms,

Math. Nachr. 281 (2008), 309-324.

[6] J. Garcfa-Cuerva and M. J. L. Herrero, A theory of Hardy spaces associated to the

Herz spaces, Proc. London Math. Soc. 69 (1994), 605-628.

[7] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities. 2d ed. Cambridge, at the

University Press, 1952. xii+324 pp.

[8] C. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier

transforms, J. Math. Mech. 18 (1968), 283-324.

[9] A. Kufner and B. Opie, Hardy-type inequalities, Pitman Research Notes in Mathematics Series, vol. 219, Longman Group UK Limited, London, 1990.

71

[10] A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientific,

Singapore, 2003.

[11] V.G. Maz'ya, Sobolev Spaces, Springer, Heidelberg, 2011.

[12] Y. Mizuta, Potential theory in Euclidean spaces, Gakkotosho, Tokyo, 1996.

[13] Y. Mizuta and T. Ohno, Sobolev's theorem and duality for Herz-Morrey spaces of

variable exponent, Ann. Acad. Sci. Fenn. Math. 39 (2014), 389-416.

[14] Y. Mizuta and T. Ohno, Herz-Morrey spaces of variable exponent, Riesz potential

operator and duality, Complex Var. Elliptic Equ. 60 (2015), no. 2, 211-240.

[15] Y. Mizuta, T. Ohno and T. Shimomura, Weak estimates for the maximal and Riesz

potential operators in non-homogeneous central Herz-Morrey spaces, Complex Var.

Elliptic Equ. 64 (2019), 1437-1456.

[16] Y. Mizuta and T. Shimomura, Hardy and Sobolev inequality in the half space, Acta

Math. Hungar. 161 (2020), 230-244.

[17] C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations,

Trans. Amer. Math. Soc. 43 (1938), 126-166.

Department of Mathematics

Graduate School of Advanced Science and Engineering

Hiroshima University

Higashi-Hiroshima 739-8521, Japan

E-mail : yomizuta@hiroshima-u.ac.jp

and

Department of Mathematics

Graduate School of Humanities and Social Sciences

Hiroshima University

Higashi-Hiroshima 739-8524, Japan

E-mail : tshimo@hiroshima-u.ac.jp

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る